M3331331 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	17.8922	67.6471%	1000000	71000000	0.7331	6.9706%	18.6253	74.6176%	11.2843%
PrimeNet	2⁶⁰	0.0461	63.3333%	14000	260000	0.0042	2.7831%	0.0503	66.1165%	2.7831%
GPU72	2⁶⁴	1.0684	65.6250%	18000	300000	0.0051	1.7536%	1.0735	67.3786%	1.7536%
Difference	+4	+16.8238	+2.0221%	+982000	+70700000	+0.7280	+5.2170%	+17.5518	+7.2391%	+7.2391%

	GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
3331331	26650649	8	24.668	4 2²	4	4	-	6.715e-13	6.092e-7	1.240e-6
3331331	1307405400736079620601	22	70.147	196228684681300 2² × 5² × 61 × 1453 × 22139461	1453	22139461	2021-01-26	72.350	0.1839	0.3431

exponent	prime factors	composite factor	digits	bits*
3331331	26650649 1307405400736079620601	34843202435721599604690420049	29	94.815

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-01-19T03:28:57	Jocelyn Larouche	Manual testing	333133	333133		-		-	-	0.051	-	-	1.621%
2021-01-26T22:21:01	gLauss	laptop-klaus	1000000	71000000			1307405400736079620601	22	70.147	0.733	0.700	1.466	6.971%
2021-02-14T21:26:15	Jocelyn Larouche	Manual testing	333133	3664464	6	-		-	-	0.078	-	-	3.511%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-03-30T19:06:03	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.973	-	-

ECM factoring results:

Total ECM effort:	12.070 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%
30	250000	3 / 640	0.005	99.532%
35	1000000	3 / 1580	0.002	99.810%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	3	0.438
50000	6750000	3	0.507
1000000	160000000	3	11.12

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-02T08:00:40	ATH	ec2-ECMCF	50000	5000000						3	0.438
2021-02-05T18:50:11	gLauss	laptop-luise	50000	6750000						3	0.507
2021-02-06T00:43:09	gLauss	laptop-luise	1000000	160000000						3	11.12

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-04T16:39:36

Oliver Kruse

GTX-3

26650649

B786DF1732AE73__

2017-12-15T03:04:17

kkmrkkblmbrbk

c4.xlarge

26650649

B786DF1732AE73__

2021-01-26T23:07:38

gLauss

laptop-klaus

26650649

1307405400736079620601

B786DF1732AE7343

2021-01-27T07:45:02

MarkS

desktop-i7

26650649

1307405400736079620601

B786DF1732AE7343

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1000000, B2 = 71000000 (stage 2)

B1 = 1000000 (stage 1)

B1 = 333133, B2 = 3664464 (stage 2)

B1 = 333133 (stage 1)

10⁰

10¹

10²

10³

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10¹

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10³

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10⁸

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront